Diagnosis
You're right to be careful. The main lens and the surrounding infrared LEDs are behind a clear, slightly domed cover that can scratch easily. Smudges are usually fingerprints or dust.
How to Fix It
Unplug the camera first. Get a clean, soft microfiber cloth—the kind you'd use for eyeglasses or a phone screen. Gently wipe the entire front dome in a circular motion, starting from the center. Don't press hard. For stubborn spots, breathe lightly on the lens to fog it slightly, then wipe immediately with the dry cloth. That's usually enough moisture. Never spray cleaner directly onto the camera.
If That Didn't Work
If there's a residue that won't come off with a dry cloth, dampen a corner of the microfiber cloth with distilled water (not tap water), wring it out completely so it's just barely damp, and gently wipe the smudge. Immediately dry the area with the dry part of the cloth.
Heads Up
Never use window cleaner, isopropyl alcohol, or other solvents. They can damage the anti-reflective coating on the lens and the plastic dome. Also, avoid using paper towels or tissues, as they can contain wood fibers that act like sandpaper on soft plastics.